Rewrite as a simplified fraction. ${0.50\overline{3} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 503.3333...\\ 100x &= 50.3333...\end{align*}}$ Subtracting the two equations, we have: ${900x = 453}$ ${x = \dfrac{453}{900}} $ ${x = \dfrac{151}{300}} $